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Thread: Substituting when figuring out limits...

  1. #1
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    Substituting when figuring out limits...

    The question is find the limit as x approaches infinity, of x(e1/x -1)

    The solution involves letting y = 1/x, however when substituting this in, the limit becomes x approaches 0.

    What's the rules with changing the value approaching when substituting in limits, as this is not the first time I have seen this.

    Thank you xxx
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  2. #2
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    Re: Substituting when figuring out limits...

    Quote Originally Posted by princessp View Post
    The question is find the limit as x approaches infinity, of x(e1/x -1)

    The solution involves letting y = 1/x, however when substituting this in, the limit becomes x approaches 0.

    [b]No, as x approaches infinity, 1/x approaches 0 while staying positive. But y = 1/x, so it is y that is approaching 0 from the right,
    that is,  0^+.

    What's the rules with changing the value approaching when substituting in limits, as this is not the first time I have seen this.
    y = 1/x means x = 1/y


    So,

     \displaystyle\lim_{x\to\infty}x(e^{1/x} - 1) \ =

    \displaystyle\lim_{y\to\0^+}\tfrac{1}{y}(e^{y} - 1) \ =

    \displaystyle\lim_{y\to\0^+}\dfrac{e^{y} - 1}{y}
    Last edited by greg1313; Jan 4th 2017 at 03:46 PM.
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